Algebraic Number Theory

By: H. Koch, I.R. Shafarevich (Editor), A.N. Parshin (Editor)

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Paperback | 12 September 1997

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280 Pages

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From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994
"... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

Industry Reviews

From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

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Preface	p. 7
Basic Number Theory	p. 8
Orders in Algebraic Number Fields	p. 9
Rings with Divisor Theory	p. 22
Dedekind Rings	p. 27
Valuations	p. 45
Harmonic Analysis on Local and Global Fields	p. 63
Hecke L-Series and the Distribution of Prime Ideals	p. 70
Class Field Theory	p. 90
The Main Theorems of Class Field Theory	p. 92
Complex Multiplication	p. 107
Cohomology of Groups	p. 112
Proof of the Main Theorems of Class Field Theory	p. 121
Simple Algebras	p. 131
Explicit Reciprocity Laws and Symbols	p. 137
Further Results of Class Field Theory	p. 145
Galois Groups	p. 150
Cohomology of Profinite Groups	p. 151
Galois Cohomology of Local and Global Fields	p. 168
Extensions with Given Galois Groups	p. 182
Abelian Fields	p. 192
The Integers of an Abelian Field	p. 193
The Arithmetical Class Number Formula	p. 195
Iwasawa's Theory of [Gamma]-Extensions	p. 206
p-adic L-Functions	p. 211
Artin L-Functions and Galois Module Structure	p. 219
Artin L-Functions	p. 222
Galois Module Structure and Artin Root Numbers	p. 234
Fields, Domains, and Complexes	p. 237
Quadratic Residues	p. 240
Locally Compact Groups	p. 241
Bernoulli Numbers	p. 243
Tables	p. 245
References	p. 251
Author Index	p. 263
Subject Index	p. 266
Table of Contents provided by Blackwell. All Rights Reserved.

Algebraic Number Theory

At a Glance

Paperback

Industry Reviews

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How to return your order

Defective items

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